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Redman was born in Brighton.[2] Her father, Ronald, was from Yorkshire and her mother, Joan, was born in India. Redman's father died in 1980, when she was in her early twenties.[3]

Redman is badly scarred on her upper left arm as a result of an accident when she was 15 months old.[4] She was scalded with a pan of boiling turkey-and-vegetable soup and suffered burns to 75 per cent of her body. Her arm was the only part of her body permanently affected, but the trauma was so severe that she was pronounced clinically dead at the Queen Victoria Hospital in East Grinstead, Sussex.[5]

In 1984 she appeared as Marina in the BBC Shakespeare production of Pericles, Prince of Tyre opposite Mike Gwilym. She also played Maxine in Oxbridge Blues, a British television mini-series, produced by the BBC and first shown in 1984 written by Frederick Raphael. In 1985 she played Janet in the touring version of The Rocky Horror Show.[citation needed]

In 1986 she played Miss Fairfax (Gwendolen) in the BBC Drama production of The Importance Of Being Earnest by Oscar Wilde.